• Density-independent population dynamics;
  • diffusion approximation;
  • extinction;
  • IUCN red list;
  • mathematical models;
  • population decline;
  • population viability analysis;
  • stochastic exponential growth model


Simple population models are increasingly being used to predict extinction risk using historical abundance estimates. A very simple model, the stochastic exponential growth (SEG) model, is surprisingly robust. Extinction risk is commonly computed for this model using a mathematical approximation (the “diffusion approximation”) that assumes continuous breeding throughout the year, an assumption that is violated by many species. Here I show that, for an organism with seasonal breeding, the diffusion approximation systematically overestimates the extinction risk. I demonstrate the conditions generating large bias (high environmental variance, intermediate extinction risk), and reanalyze 100 populations of conservation concern. Analyzing several policy applications, I find that the bias may be most important when classifying the risk status of species. The SEG model is still sound, but associated risk estimates should be calculated by performing stochastic simulations (as with all other population viability models) rather than by evaluating the diffusion approximation.